Deflexions of Membranes, Bars, and Plates. 303 



t ?=0, the logarithm becomes infinite, but dw/dx is still zero 

 in virtue of the factor x. 



I suppose that w cannot be expressed in finite terms by 

 integration of (36), but there would be no difficulty in 

 dealing arithmetically with particular cases by direct use of 

 the series (28). If, lor example, 7) — \it, so that the force is 

 applied at the centre, we have to consider 



Sw -3 sin \nir . sin ny . e~ nx (l + nx), . . (38) 



and only odd values of n enter. Further, (38) is symmetrical 

 on the two sides of y-=\ir. Two special cases present 

 themselves when x = and when y = ±7r. In the former w 

 is proportional to 



sin?/- £- g sin 3?/+ ^ sin 5?/- ..., . . . (39) 



and in the latter to 



e~ x (l + x)+ ^3 e- & (l + 3^>) + ^3 e- Bx (l + 5a) + 



(40) 



August % 1916. 



Added August 21. 



The accompanying tables show the form of the curves of 

 deflexion defined by (39), (40). 



y> 



(39). 



y> 



(39). 



0° 



•0000 



50 



•7416 



10 



•1594 



60 



•8574 



20 



•3162 



70 



•9530 



30 



•4675 



80 



1-0217 



40 



•6104 



90 



1-0518 



X. 



(40). 



X. 



(40). 



00 



10518 



3-0 



•1992 



0-5 



•9333 



4-0 



•0916 



10 



•7435 



5-0 



•0404 



2-0 



•4066 



100 



•0005 



In a second communication * Mesnager returns to the 

 question and shows by very simple reasoning that all points 



* C. R. July 24, 1916, p. 84. 



